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goodwill
Sep 15, 2006, 3:02 PM
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Recently I started pondering the physics involved in slacklining, and particularly the kinds of forces that highlining anchors have to withstand. I started to work out some equations for these forces, first in simple cases, then in more complicated ones. One thing led to another, and before I knew it, I had written a 22-page paper on the subject. This is entirely theoretical stuff, guided by my own experience with slacklining, but with no experimental data to back it up. It does make one linearity assumption that may be completely invalid for nylon webbing, but the payoff is that everything can then be calculated in terms of a few geometric measurements.
Some of the conclusions I came to were surprising, to me anyway. For example, in the case of taking a leash fall on a highline, the forces on the anchors are not actually that much higher than when you're just standing or walking on the line, except when the fall occurs very close to one anchor (like within a few feet). In that case, the force on the near anchor might be doubled during the fall, but the force on the far anchor will barely change at all.
Another interesting fact is that, when you're just walking on the line, the forces on the anchors don't change very much as you move from one end of the line to the other. The force on an anchor is lowest when you're at the opposite end of the line, and increases steadily as you approach the anchor, but the total change from one end to the other is usually less than 12%.
And a fact that's just plain fascinating if you're a math geek like me, but totally worthless otherwise, is this: if the big linearity assumption I mentioned is completely true, then the path that your body takes as you walk from one end of the line to the other is a perfect parabola.
Again, all of this is based on an assumption that may not be true at all. I'm hoping to have a chance to test this assumption experimentally at some point, but for now that will have to wait. But I'm curious, does anyone have any data that contradicts these claims?
I also have written a little web-based force calculator. I know one of these already exists, but its capabilities are very limited compared to this one. You can check it out at http://will.is-a-geek.org/...ining/calculator.php
If you're interested in reading the paper, I would welcome any feedback. Take the link above, and you can download the PDF from there. If you want to skip all the math, start with the discussion in section 3.3, or just skip right to the results in section 4.
Will
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slackinghigh
Sep 15, 2006, 4:31 PM
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Alright!!! I just read your paper and used your calculator. Results seemed pretty reasonable given the tension rumors out there. Lots of numbers . . . I'm glad you did it!
Thanks for posting your results, and we will have to get you some "real world" tension measurements on the anchors to see how it all holds up. Very cool!
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slacklinejoe
Sep 15, 2006, 4:47 PM
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Will,
You've got a very intereting write up on the topic. I'll have to spend a few days absorbing it all to really break it all down. You seem to have noted all of my immediate concerns about accuracy of the calculations (dynamic leash & variance in line elongation) as exceptions in your calculations.
If I can find one for a reasonable amount I plan on investing in a dynamometer to field test these theories. If anyone spots one capable of doing 10K lbs let me know. I doubt I'd have the cash for a wireless digital but a used analog with a max load marker would meet my needs.
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bues0022
Sep 15, 2006, 7:10 PM
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I find it quite interesting that you wrote a scholarly paper on a topic that most would find not. I'm in the process of reading it right now, very interesting, especially for a fellow geek like myself.
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goodwill
Sep 15, 2006, 10:06 PM
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In reply to: I find it quite interesting that you wrote a scholarly paper on a topic that most would find not.
Yeah, I know that's kinda funny. I wanted to post my findings online, and with all the math, I figured the easiest way to do that would be to use Latex. And that's just the way Latex formats things. As far as the writing style being scholarly, as an aspiring mathematician, that's just the way I'm used to writing. But you're right, the content is hardly what I'd call "scholarly".
Joe, I'm glad to hear you that you endeavor to do this kind of testing. In my opinion, it's really something the slacklining community needs. If I happen to see any inexpensive dynamometers for sale, I'll let you know.
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slacklinejoe
Sep 19, 2006, 7:15 PM
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FYI: I just purchased a dynamometer. Testing will ensue as soon as it arrives.
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jimdavis
Sep 25, 2006, 3:44 AM
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Will, that's really cool that you put that out there. One suggestion I would make though is to label and specify the units for distance and weight and all. I was assuming feet and pounds, but I'm sure there are people that would plug in meters and newtons without a second thought.
Cheers,
Jim
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slacklinejoe
Sep 25, 2006, 3:53 AM
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In reply to: Will, that's really cool that you put that out there. One suggestion I would make though is to label and specify the units for distance and weight and all. I was assuming feet and pounds, but I'm sure there are people that would plug in meters and newtons without a second thought. Cheers, Jim
Well, the equation doesn't really require it to be in metric or standard as long as you use the same units for the answer.
So as long as you are consistent for all types of lengths or force you'll get the right answer as long as you expect it to output into the same unit type. That's kind of the beauty of the equation. He could label it one or the other for less thinking on the users part, but in reality it'll work fine either way.
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jimdavis
Sep 25, 2006, 3:58 AM
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Yeah, I kinda figured that....but considering how much climbers talk about weight in pounds, and force in newtons.....just thought it might be nice to make it a little clearer.
All the same though, I guess.
Jim
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niles
Sep 25, 2006, 6:20 AM
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This is cool! We might actually be on the brink of getting some real results to a question that has been up in the air for a long time now! Good job guys, keep us lesser minds informed!
Niles
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slacker_jon
Dec 19, 2006, 12:42 PM
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In reply to: FYI: I just purchased a dynamometer. Testing will ensue as soon as it arrives.
Joe, did you ever do any testing?
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slackinghigh
Dec 19, 2006, 2:20 PM
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Awsome man,
It will be nice to know how close we are really pushing limits that shouldn't be broken. Have fun testing!
Dylan
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slacklinejoe
Dec 19, 2006, 2:43 PM
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slacker_jon wrote: In reply to: FYI: I just purchased a dynamometer. Testing will ensue as soon as it arrives. Joe, did you ever do any testing?
Damn Dynometer was broken (out of calibration by 7,000 lbs) when listed as "same as new". I've tried to buy a couple others but always have been outbid. I will buy one as soon as things get a little less hectic (working 60+hrs / week right now). Once I get my testing done, I'd be glad to loan it out for others needing to run their own experiments (with deposit though, things get out of calibration with too much jarring around).
(This post was edited by slacklinejoe on Dec 19, 2006, 2:48 PM)
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